Consider a container that contains a mixture of many liquids. Can two of these liquids phase separate without having any significant effect on other liquids inside the container? Is there a feasible scenario where the above can actually happen? I am interested in a scenario where the two liquids only separates themselves from each other and not the rest of the mixture.

More precisely:
Assume the container contains a mixture of liquids A and B with many other liquids (state 1). Can these two liquids separate (triggered by change in the pressure, temperature, ...) so that at the end (state 2) the liquids in the container are divided into two regions with the following properties:

The first region does not contain liquid B. It contains liquid A with the exact same mixture of the other liquid (same as state 1).

The second region does not contain liquid A. It contains liquid B with the same mixture of other liquids (same as state 1).

Indeed we want other liquids in the container to be neutral to the phase separation of the liquids A and B.

3 Answers
3

I don't think what you are asking for is thermodynamically impossible, but I think it is very unlikely. Let's say you start off with a single liquid phase containing molecules A, B, X, Y, and Z.

Let's also say that when temperature changes, two phases form. One phase is mostly A and the other phase is mostly B. Let's call those two phases $a$ and $b$. Your question is, is there some condition where the concentrations of molecules X, Y, and Z in phase $a$ is the same as it is in phase $b$.

In general the distribution of a solute between two phases is governed by a parameter called a partition coefficient or a distribution constant. The distribution of molecule X in phase $a$ vs phase $b$, for example, could be noted as $K_{ab, X}$. For your condition to be satisified, the distribution coefficient of X would have to be 1.0, i.e. it would have an equal preference for both phases. The same would be true of molecules Y and Z, i.e. $K_{ab, X}=K_{ab, Y}=K_{ab, Z}=1$ is required for your condition.

A common type of liquid phase separation is oil and water: they don't mix. I can't think of three molecules that each have an equal preference for water vs. oil. These molecules would be somewhat hydrophobic and somewhat hydrophilic. Feel free to look through a giant compendium of octanol-water partition coefficients published by NIST to look for three molecules X, Y, and Z that all have octanol-water partition coefficients of 1.0 by yourself, though.

Natural separation term is not a good one but i'm gonna use it here. If at equilibrium (When the free energy of all the chemical constituents are same), those two specific liquid like to separate themselves out from the rest of the mixture, than you just need to give it enough time to reach equilibrium to separate them out. And this is the only method i can think of which will have no significant effect on the liquid in that container.

Forced:

Forced separation: Now if the above mentioned equilibrium condition needs different temp. and pressure than room temp. and pressure. Then by simply changing temp. and pressure you can achieve the above separation. Or you can utilize the different in various properties to separate them, e.g. Viscosity, boiling point, melting point etc.
Distillation: If they have separate boiling point than you can use distillation column and collecting the liquid at various height will give you separated solvent.
Solvent extraction, Filtration, mixer settlers, centrifugal force, ion exchange, membrane filtration, using bio separation like algae etc you can also achieve liquid liquid extraction.

I tried to answer the above comment but couldn't due to character limitation. So, i'm posting it here as another answer:
To answer your question we need more data. For example if we want to separate mixture of sand and sugar, we can utilize the solubility difference of these two substances. To separate water and salt, we use heat to vaporize water but that doesn't mean salt is non-volatile. Salt can be vaporized but at very high temp. (As far i can remember mp of NaCl is around 800 deg C and bp is 1500 deg C. So, if you use temp. greater than 1500 deg C to separate water and NaCl, then you will end up with a mixture of vapor of water and salt. So, in room temp. your desired separation will happen or not or do we need to exploit any physical properties, we need to know their properties. If you know the mixture components, than use CRC or Perry's handbook to find out their behavior. Even you can also find multiple component phase diagram, which will tell you everything about the mixture. Or if their is no data available, you can use software like HYSYS to exploit the QSPR.